Abstract

The gas flow between two concentric rotating cylinders is considered in order to investigate non-equilibrium effects associated with the Knudsen layers over curved surfaces. We investigate the nonlinear flow physics in the near-wall regions using a new power-law (PL) wall-scaling approach. This PL model incorporates Knudsen layer effects in near-wall regions by taking into account the boundary limiting effects on the molecular free paths. We also report new direct simulation Monte Carlo results covering a wide range of Knudsen numbers and accommodation coefficients, and for various outer-to-inner cylinder radius ratios. Our simulation data are compared with both the classical slip flow theory and the PL model, and we find that non-equilibrium effects are not only dependent on Knudsen number and accommodation coefficient but are also significantly affected by the surface curvature. The relative merits and limitations of both theoretical models are explored with respect to rarefaction and curvature effects. The PL model is able to capture some of the nonlinear trends associated with Knudsen layers up to the early transition flow regime. The present study also illuminates the limitations of classical slip flow theory even in the early slip flow regime for higher curvature test cases, although the model does exhibit good agreement throughout the slip flow regime for lower curvature cases. Torque and velocity profile comparisons also convey that a good prediction of integral flow properties does not necessarily guarantee the accuracy of the theoretical model used, and it is important to demonstrate that field variables are also predicted satisfactorily.

Received 26 November 2012Accepted 22 April 2013Published online 23 May 2013

Acknowledgments:

The research leading to these results has received funding from the European Community's Seventh Framework Programme FP7/2007-2013 under grant agreement ITN GASMEMS (Grant Agreement No. 215504). The author C.W. gratefully acknowledges funding from the James Weir Foundation. The author J.M.R. gratefully acknowledges funding through EPSRC Programme Grant EP/I011927/1. Our calculations were performed on the 1100 core HPC Facility of the Faculty of Engineering at the University of Strathclyde. The authors thank the reviewers for their useful comments.